Residue Structures
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913268722827264 |
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| author | Rowen, Louis H. |
| author_facet | Rowen, Louis H. |
| contents | We consider residue structures $R/G$ where $(G,+)$ is an additive subgroup of a ring $(R,+,\cdot)$, not necessarily an ideal. Special instances include Krasner's construction of quotient hyperfields, and Pumpluen's construction of nonassociative algebras. The residue construction, treated formally, satisfies the Noether isomorphism theorems, and also is cast in a broader categorical setting which includes categorical products, sums, and tensor products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Residue Structures Rowen, Louis H. Rings and Algebras Primary 16Y20, 16Y60, 16W99, Secondary 14T10, 20N20 We consider residue structures $R/G$ where $(G,+)$ is an additive subgroup of a ring $(R,+,\cdot)$, not necessarily an ideal. Special instances include Krasner's construction of quotient hyperfields, and Pumpluen's construction of nonassociative algebras. The residue construction, treated formally, satisfies the Noether isomorphism theorems, and also is cast in a broader categorical setting which includes categorical products, sums, and tensor products. |
| title | Residue Structures |
| topic | Rings and Algebras Primary 16Y20, 16Y60, 16W99, Secondary 14T10, 20N20 |
| url | https://arxiv.org/abs/2403.09467 |